Filtered Multiplicative Bases of Restricted Enveloping Algebras

We study the problem of the existence of filtered multiplicative bases of a restricted enveloping algebra u(L), where L is a finite-dimensional and p-nilpotent restricted Lie algebra over a field of positive characteristic p.

The SARS algorithm: detrending CoRoT light curves with Sysrem using simultaneous external parameters

Surveys for exoplanetary transits are usually limited not by photon noise but rather by the amount of red noise in their data. In particular, although the CoRoT space-based survey data are being carefully scrutinized, significant new sources of systematic noises are still being discovered. Recently, a magnitude-dependant systematic effect was discovered in the CoRoT data by Mazeh et al. and a phenomenological correction was proposed. Here we tie the observed effect to a particular type of effect, and in the process generalize the popular Sysrem algorithm to include external parameters in a simultaneous solution with the unknown effects. We show that a post-processing scheme based on this algorithm performs well and indeed allows for the detection of new transit-like signals that were not previously detected.

Consistency in approximate entropy given by a volumetric estimate

Non-linear methods for estimating variability in time-series are currently of widespread use. Among such methods are approximate entropy (ApEn) and sample approximate entropy (SampEn). The applicability of ApEn and SampEn in analyzing data is evident and their use is increasing. However, consistency is a point of concern in these tools, i.e., the classification of the temporal organization of a data set might indicate a relative less ordered series in relation to another when the opposite is true. As highlighted by their proponents themselves, ApEn and SampEn might present incorrect results due to this lack of consistency. In this study, we present a method which gains consistency by using ApEn repeatedly in a wide range of combinations of window lengths and matching error tolerance. The tool is called volumetric approximate entropy, vApEn. We analyze nine artificially generated prototypical time-series with different degrees of temporal order (combinations of sine waves, logistic maps with different control parameter values, random noises). While ApEn/SampEn clearly fail to consistently identify the temporal order of the sequences, vApEn correctly do. In order to validate the tool we performed shuffled and surrogate data analysis. Statistical analysis confirmed the consistency of the method. (C) 2008 Elsevier Ltd. All rights reserved.

Growth, encystment and survival of Acanthamoeba castellanii grazing on different bacteria

Free-living amoebae of the genus Acanthamoeba are widely distributed in soil and water collections, where trophozoites (vegetative, multiplicative stages) feed mainly by phagocytosis and thus control bacterial populations in the environment. Here, we examined the growth, encystment and survival of Acanthamoeba castellanii receiving different bacteria (Escherichia coli, Pseudomonas aeruginosa, Enterobacter cloacae, Bacillus subtilis, Bacillus megaterium, Micrococcus luteus, and Staphylococcus aureus) in nonnutrient saline. All bacteria assayed induced a dose-dependent proliferative response, in most cases maximized with a bacterial dose of 1 x 10(9) mL(-1); except for M. luteus, trophozoites grew better with viable than with heat-killed bacteria. In addition, Acanthamoeba growth was improved by adding bacteria on alternate days. Single-dose experiments indicated a temporal association between the growth of trophozoite and bacterial consumption, and higher consumption of M. luteus, E. coli and P. aeruginosa, bacterial species that allowed the highest trophozoite yields. Long-term Acanthamoeba-bacteria incubation revealed that encystment was significantly delayed by almost all the bacteria assayed (including S. aureus, which elicited a poor growth response) and that the presence of bacteria markedly increased cyst yield; final cyst recovery clearly depended on both the dose and the type of the bacterium given, being much higher with E. coli, M. luteus and P. aeruginosa.

A NOTE ON FREE GROUPS IN THE RING OF FRACTIONS OF SKEW POLYNOMIAL RINGS

Let L be a function field over the rationals and let D denote the skew field of fractions of L[t; sigma], the skew polynomial ring in t, over L, with automorphism sigma. We prove that the multiplicative group D(x) of D contains a free noncyclic subgroup.